摘要
[J.Optim.Theory Appl.,2002,114(2):287-343]在严格极小点和伪正则条件下建立了约束优化问题的精确罚性质.本文中我们给出了一个改进的精确罚结果,即约束优化问题在任意非严格局部极小点和伪正则条件下具有精确罚性质.借鉴这种思想,我们也改进了[SIAM J.Optim.,2010,20(5):2730-2753]中均衡约束优化问题的精确罚结果,在MPEC广义伪正规条件下证明了均衡约束优化问题的精确罚结果仍然成立,相比[SIAM J.Optim.,2010,20(5):2730-2753]中的工作,我们的证明更为简单,而且不需要用到Ekeland变分原理.
In[J.Optim.Theory Appl.,2002,114(2):287-343],the authors proved that any strict local minimum of the constrained optimization possesses the exact penalty property under the assumption of pseudonormality.In this paper,we present an improved exact penalty result,i.e.,any nonstrict local minimum of the constrained optimization admits the exact penalty property under the same conditions.Following the same idea,we also investigate the exact penalty property of mathematical program with equilibrium constraints(MPEC)in[SIAM J.Optim.,2010,20(5):2730-2753].An alternative proof is provided for the exact penalty result of MPEC under the condition of MPEC generalized pseudonormality,and our proof does not use the Ekeland variational principle and is elementary.
作者
陈玉
罗小虎
胡清洁
CHEN Yu;LUO Xiaohu;HU Qingjie(School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi,541004,P.R.China;Center for Applied Mathematics of Guangxi,Guangxi Normal University,Guilin,Guangxi,541004,P.R.China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin,Guangxi,541004,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第4期729-740,共12页
Advances in Mathematics（China）
基金
Supported by NSFC(Nos.11761014,11961011)
Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001)
关键词
约束优化
伪正则
非严格极小
精确罚
constrained optimization
pseudonormality
nonstrict local minimum
exact penalty
作者简介
陈玉,E-mail:chenyu4660@163.com;胡清洁,E-mail:hqj0715@126.com
